We describe a system of stochastic differential equations (SDEs) which model
the interaction between processive molecular motors, such as kinesin and
dynein, and the biomolecular cargo they tow as part of microtubule-based
intracellular transport. We show that the classical experimental environment
fits within a parameter regime which is qualitatively distinct from conditions
one expects to find in living cells. Through an asymptotic analysis of our
system of SDEs, we develop a means for applying in vitro observations of the
nonlinear response by motors to forces induced on the attached cargo to make
analytical predictions for two parameter regimes that have thus far eluded
direct experimental observation: 1) highly viscous in vivo transport and 2)
dynamics when multiple identical motors are attached to the cargo and
microtubule